An efficient parallel iteration algorithm for nonlinear diffusion equations with time extrapolation techniques and the Jacobi explicit scheme

Abstract

To numerically simulate the radiation diffusion problem with high parallel efficiency, we present a new parallel iteration algorithm for nonlinear diffusion equations. The algorithm is based on the domain decomposition method, and it integrates time extrapolation techniques and an advanced Jacobi explicit scheme. The domain decomposition method decomposes a large global problem into multiple sub-problems which can be solved on multiple processors in parallel. The time extrapolation technique gives the prediction values with the second or third order accuracy in time for the current time layer by specific combinations of the previous two or three time layers. The advanced Jacobi explicit scheme further improves the precision of the prediction values. Overall, the proposed algorithm makes the prediction values of the inner boundary more reasonable and offers accurate iterative initial values for all cells, which reduces the number of nonlinear iterations and improves the parallel computation efficiency remarkably.